105 citations · 254 across the 20 of their papers we have counts for
11 papers · 1 filter
Subcritical monotone cellular automata
Paul Balister, Béla Bollobás, Robert Morris +1
We study monotone cellular automata (also known as -bootstrap percolation) in with random initial configurations. Confirming a conjecture of Balister, B…
A local limit theorem for Quicksort key comparisons via multi-round smoothing
Béla Bollobás, James Allen Fill, Oliver Riordan
As proved by Régnier and Rösler, the number of key comparisons required by the randomized sorting algorithm QuickSort to sort a list of distinct items (keys) satisfies a global…
Coalescence on the real line
Paul Balister, Béla Bollobás, Jonathan Lee +1
We study a geometrically constrained coalescence model derived from spin systems. Given two probability distributions and on the positive reals with f…
The sharp threshold for the Duarte model
Béla Bollobás, Hugo Duminil-Copin, Robert Morris +1
The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollobás, Smith and Uzzell, and the critical threshold for percolation was determine…
Consistent random vertex-orderings of graphs
Paul Balister, Béla Bollobás, Svante Janson
Given a hereditary graph property , consider distributions of random orderings of vertices of graphs that are preserved under isomorphisms and under…
Universality for two-dimensional critical cellular automata
Béla Bollobás, Hugo Duminil-Copin, Robert Morris +1
We study the class of monotone, two-state, deterministic cellular automata, in which sites are activated (or 'infected') by certain configurations of nearby infected sites. These m…